A free boundary problem arising in superconductor modeling

Article type: Research Article

Authors: Friedman, Avner^; | Hu, Bei

Affiliations: Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, USA | Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA

Note: [] This work is partially supported by NSF Grant DMS-86-12880.

Abstract: By gradually decreasing the ambient magnetic field, under isothermal conditions, a superconductor material (of “type I”) will develop two phases separated by a thin interface Γ(t). In the “normal” conducting phase the magnetic field $\vec{H}$ is divergence free and satisfies the heat equation, whereas on the interface Γ(t), curl $\vec{H}\times n=-V_{n}\vec{H}$ where n is the normal and Vn the velocity of Γ(t); further, $|\vec{H}|=H_{c}$ (constant) on Γ(t). This free boundary problem is studied in the present paper. Existence, uniqueness and asymptotic behavior are established under assumptions which enable us to reduce the 3-dimensional problem to a problem depending on essentially one-dimensional space variable.

DOI: 10.3233/ASY-1992-6201

Journal: Asymptotic Analysis, vol. 6, no. 2, pp. 109-133, 1992